Research Interests

My area of research is number theory, especially the theory of
automorphic forms. I am also
interested
in several related areas, such as algebraic geometry and representation theory.

``It is a deeper subject than I appreciated and, I begin to suspect,
deeper than anyone yet appreciates.
To see it whole is certainly a daunting,
for the moment even impossible, task.''
(Robert Langlands, writing about the theory of automorphic forms.)

A concise description of Tate's geometric reformation of the BSD conjecture in the function field case, together with the main conjecture of Iwasawa theory for elliptic curves,
which is an analogue of Tate's conjecture in the context of
elliptic curves over number fields.

A brief discussion of Dwork's p-adic methods in arithmetic geometry,
and the modern theories that they helped to give rise to.
(My contribution to this discussion
gives a related
overview of the historical context of the development of p-adic Hoge theory.)